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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.stat.clustering;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import java.util.ArrayList;<a name="line.20"></a>
<FONT color="green">021</FONT>    import java.util.Collection;<a name="line.21"></a>
<FONT color="green">022</FONT>    import java.util.Collections;<a name="line.22"></a>
<FONT color="green">023</FONT>    import java.util.List;<a name="line.23"></a>
<FONT color="green">024</FONT>    import java.util.Random;<a name="line.24"></a>
<FONT color="green">025</FONT>    <a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.ConvergenceException;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.exception.MathIllegalArgumentException;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.stat.descriptive.moment.Variance;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math3.util.MathUtils;<a name="line.31"></a>
<FONT color="green">032</FONT>    <a name="line.32"></a>
<FONT color="green">033</FONT>    /**<a name="line.33"></a>
<FONT color="green">034</FONT>     * Clustering algorithm based on David Arthur and Sergei Vassilvitski k-means++ algorithm.<a name="line.34"></a>
<FONT color="green">035</FONT>     * @param &lt;T&gt; type of the points to cluster<a name="line.35"></a>
<FONT color="green">036</FONT>     * @see &lt;a href="http://en.wikipedia.org/wiki/K-means%2B%2B"&gt;K-means++ (wikipedia)&lt;/a&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>     * @version $Id: KMeansPlusPlusClusterer.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.37"></a>
<FONT color="green">038</FONT>     * @since 2.0<a name="line.38"></a>
<FONT color="green">039</FONT>     */<a name="line.39"></a>
<FONT color="green">040</FONT>    public class KMeansPlusPlusClusterer&lt;T extends Clusterable&lt;T&gt;&gt; {<a name="line.40"></a>
<FONT color="green">041</FONT>    <a name="line.41"></a>
<FONT color="green">042</FONT>        /** Strategies to use for replacing an empty cluster. */<a name="line.42"></a>
<FONT color="green">043</FONT>        public static enum EmptyClusterStrategy {<a name="line.43"></a>
<FONT color="green">044</FONT>    <a name="line.44"></a>
<FONT color="green">045</FONT>            /** Split the cluster with largest distance variance. */<a name="line.45"></a>
<FONT color="green">046</FONT>            LARGEST_VARIANCE,<a name="line.46"></a>
<FONT color="green">047</FONT>    <a name="line.47"></a>
<FONT color="green">048</FONT>            /** Split the cluster with largest number of points. */<a name="line.48"></a>
<FONT color="green">049</FONT>            LARGEST_POINTS_NUMBER,<a name="line.49"></a>
<FONT color="green">050</FONT>    <a name="line.50"></a>
<FONT color="green">051</FONT>            /** Create a cluster around the point farthest from its centroid. */<a name="line.51"></a>
<FONT color="green">052</FONT>            FARTHEST_POINT,<a name="line.52"></a>
<FONT color="green">053</FONT>    <a name="line.53"></a>
<FONT color="green">054</FONT>            /** Generate an error. */<a name="line.54"></a>
<FONT color="green">055</FONT>            ERROR<a name="line.55"></a>
<FONT color="green">056</FONT>    <a name="line.56"></a>
<FONT color="green">057</FONT>        }<a name="line.57"></a>
<FONT color="green">058</FONT>    <a name="line.58"></a>
<FONT color="green">059</FONT>        /** Random generator for choosing initial centers. */<a name="line.59"></a>
<FONT color="green">060</FONT>        private final Random random;<a name="line.60"></a>
<FONT color="green">061</FONT>    <a name="line.61"></a>
<FONT color="green">062</FONT>        /** Selected strategy for empty clusters. */<a name="line.62"></a>
<FONT color="green">063</FONT>        private final EmptyClusterStrategy emptyStrategy;<a name="line.63"></a>
<FONT color="green">064</FONT>    <a name="line.64"></a>
<FONT color="green">065</FONT>        /** Build a clusterer.<a name="line.65"></a>
<FONT color="green">066</FONT>         * &lt;p&gt;<a name="line.66"></a>
<FONT color="green">067</FONT>         * The default strategy for handling empty clusters that may appear during<a name="line.67"></a>
<FONT color="green">068</FONT>         * algorithm iterations is to split the cluster with largest distance variance.<a name="line.68"></a>
<FONT color="green">069</FONT>         * &lt;/p&gt;<a name="line.69"></a>
<FONT color="green">070</FONT>         * @param random random generator to use for choosing initial centers<a name="line.70"></a>
<FONT color="green">071</FONT>         */<a name="line.71"></a>
<FONT color="green">072</FONT>        public KMeansPlusPlusClusterer(final Random random) {<a name="line.72"></a>
<FONT color="green">073</FONT>            this(random, EmptyClusterStrategy.LARGEST_VARIANCE);<a name="line.73"></a>
<FONT color="green">074</FONT>        }<a name="line.74"></a>
<FONT color="green">075</FONT>    <a name="line.75"></a>
<FONT color="green">076</FONT>        /** Build a clusterer.<a name="line.76"></a>
<FONT color="green">077</FONT>         * @param random random generator to use for choosing initial centers<a name="line.77"></a>
<FONT color="green">078</FONT>         * @param emptyStrategy strategy to use for handling empty clusters that<a name="line.78"></a>
<FONT color="green">079</FONT>         * may appear during algorithm iterations<a name="line.79"></a>
<FONT color="green">080</FONT>         * @since 2.2<a name="line.80"></a>
<FONT color="green">081</FONT>         */<a name="line.81"></a>
<FONT color="green">082</FONT>        public KMeansPlusPlusClusterer(final Random random, final EmptyClusterStrategy emptyStrategy) {<a name="line.82"></a>
<FONT color="green">083</FONT>            this.random        = random;<a name="line.83"></a>
<FONT color="green">084</FONT>            this.emptyStrategy = emptyStrategy;<a name="line.84"></a>
<FONT color="green">085</FONT>        }<a name="line.85"></a>
<FONT color="green">086</FONT>    <a name="line.86"></a>
<FONT color="green">087</FONT>        /**<a name="line.87"></a>
<FONT color="green">088</FONT>         * Runs the K-means++ clustering algorithm.<a name="line.88"></a>
<FONT color="green">089</FONT>         *<a name="line.89"></a>
<FONT color="green">090</FONT>         * @param points the points to cluster<a name="line.90"></a>
<FONT color="green">091</FONT>         * @param k the number of clusters to split the data into<a name="line.91"></a>
<FONT color="green">092</FONT>         * @param numTrials number of trial runs<a name="line.92"></a>
<FONT color="green">093</FONT>         * @param maxIterationsPerTrial the maximum number of iterations to run the algorithm<a name="line.93"></a>
<FONT color="green">094</FONT>         *     for at each trial run.  If negative, no maximum will be used<a name="line.94"></a>
<FONT color="green">095</FONT>         * @return a list of clusters containing the points<a name="line.95"></a>
<FONT color="green">096</FONT>         * @throws MathIllegalArgumentException if the data points are null or the number<a name="line.96"></a>
<FONT color="green">097</FONT>         *     of clusters is larger than the number of data points<a name="line.97"></a>
<FONT color="green">098</FONT>         * @throws ConvergenceException if an empty cluster is encountered and the<a name="line.98"></a>
<FONT color="green">099</FONT>         * {@link #emptyStrategy} is set to {@code ERROR}<a name="line.99"></a>
<FONT color="green">100</FONT>         */<a name="line.100"></a>
<FONT color="green">101</FONT>        public List&lt;Cluster&lt;T&gt;&gt; cluster(final Collection&lt;T&gt; points, final int k,<a name="line.101"></a>
<FONT color="green">102</FONT>                                        int numTrials, int maxIterationsPerTrial)<a name="line.102"></a>
<FONT color="green">103</FONT>            throws MathIllegalArgumentException, ConvergenceException {<a name="line.103"></a>
<FONT color="green">104</FONT>    <a name="line.104"></a>
<FONT color="green">105</FONT>            // at first, we have not found any clusters list yet<a name="line.105"></a>
<FONT color="green">106</FONT>            List&lt;Cluster&lt;T&gt;&gt; best = null;<a name="line.106"></a>
<FONT color="green">107</FONT>            double bestVarianceSum = Double.POSITIVE_INFINITY;<a name="line.107"></a>
<FONT color="green">108</FONT>    <a name="line.108"></a>
<FONT color="green">109</FONT>            // do several clustering trials<a name="line.109"></a>
<FONT color="green">110</FONT>            for (int i = 0; i &lt; numTrials; ++i) {<a name="line.110"></a>
<FONT color="green">111</FONT>    <a name="line.111"></a>
<FONT color="green">112</FONT>                // compute a clusters list<a name="line.112"></a>
<FONT color="green">113</FONT>                List&lt;Cluster&lt;T&gt;&gt; clusters = cluster(points, k, maxIterationsPerTrial);<a name="line.113"></a>
<FONT color="green">114</FONT>    <a name="line.114"></a>
<FONT color="green">115</FONT>                // compute the variance of the current list<a name="line.115"></a>
<FONT color="green">116</FONT>                double varianceSum = 0.0;<a name="line.116"></a>
<FONT color="green">117</FONT>                for (final Cluster&lt;T&gt; cluster : clusters) {<a name="line.117"></a>
<FONT color="green">118</FONT>                    if (!cluster.getPoints().isEmpty()) {<a name="line.118"></a>
<FONT color="green">119</FONT>    <a name="line.119"></a>
<FONT color="green">120</FONT>                        // compute the distance variance of the current cluster<a name="line.120"></a>
<FONT color="green">121</FONT>                        final T center = cluster.getCenter();<a name="line.121"></a>
<FONT color="green">122</FONT>                        final Variance stat = new Variance();<a name="line.122"></a>
<FONT color="green">123</FONT>                        for (final T point : cluster.getPoints()) {<a name="line.123"></a>
<FONT color="green">124</FONT>                            stat.increment(point.distanceFrom(center));<a name="line.124"></a>
<FONT color="green">125</FONT>                        }<a name="line.125"></a>
<FONT color="green">126</FONT>                        varianceSum += stat.getResult();<a name="line.126"></a>
<FONT color="green">127</FONT>    <a name="line.127"></a>
<FONT color="green">128</FONT>                    }<a name="line.128"></a>
<FONT color="green">129</FONT>                }<a name="line.129"></a>
<FONT color="green">130</FONT>    <a name="line.130"></a>
<FONT color="green">131</FONT>                if (varianceSum &lt;= bestVarianceSum) {<a name="line.131"></a>
<FONT color="green">132</FONT>                    // this one is the best we have found so far, remember it<a name="line.132"></a>
<FONT color="green">133</FONT>                    best            = clusters;<a name="line.133"></a>
<FONT color="green">134</FONT>                    bestVarianceSum = varianceSum;<a name="line.134"></a>
<FONT color="green">135</FONT>                }<a name="line.135"></a>
<FONT color="green">136</FONT>    <a name="line.136"></a>
<FONT color="green">137</FONT>            }<a name="line.137"></a>
<FONT color="green">138</FONT>    <a name="line.138"></a>
<FONT color="green">139</FONT>            // return the best clusters list found<a name="line.139"></a>
<FONT color="green">140</FONT>            return best;<a name="line.140"></a>
<FONT color="green">141</FONT>    <a name="line.141"></a>
<FONT color="green">142</FONT>        }<a name="line.142"></a>
<FONT color="green">143</FONT>    <a name="line.143"></a>
<FONT color="green">144</FONT>        /**<a name="line.144"></a>
<FONT color="green">145</FONT>         * Runs the K-means++ clustering algorithm.<a name="line.145"></a>
<FONT color="green">146</FONT>         *<a name="line.146"></a>
<FONT color="green">147</FONT>         * @param points the points to cluster<a name="line.147"></a>
<FONT color="green">148</FONT>         * @param k the number of clusters to split the data into<a name="line.148"></a>
<FONT color="green">149</FONT>         * @param maxIterations the maximum number of iterations to run the algorithm<a name="line.149"></a>
<FONT color="green">150</FONT>         *     for.  If negative, no maximum will be used<a name="line.150"></a>
<FONT color="green">151</FONT>         * @return a list of clusters containing the points<a name="line.151"></a>
<FONT color="green">152</FONT>         * @throws MathIllegalArgumentException if the data points are null or the number<a name="line.152"></a>
<FONT color="green">153</FONT>         *     of clusters is larger than the number of data points<a name="line.153"></a>
<FONT color="green">154</FONT>         * @throws ConvergenceException if an empty cluster is encountered and the<a name="line.154"></a>
<FONT color="green">155</FONT>         * {@link #emptyStrategy} is set to {@code ERROR}<a name="line.155"></a>
<FONT color="green">156</FONT>         */<a name="line.156"></a>
<FONT color="green">157</FONT>        public List&lt;Cluster&lt;T&gt;&gt; cluster(final Collection&lt;T&gt; points, final int k,<a name="line.157"></a>
<FONT color="green">158</FONT>                                        final int maxIterations)<a name="line.158"></a>
<FONT color="green">159</FONT>            throws MathIllegalArgumentException, ConvergenceException {<a name="line.159"></a>
<FONT color="green">160</FONT>    <a name="line.160"></a>
<FONT color="green">161</FONT>            // sanity checks<a name="line.161"></a>
<FONT color="green">162</FONT>            MathUtils.checkNotNull(points);<a name="line.162"></a>
<FONT color="green">163</FONT>    <a name="line.163"></a>
<FONT color="green">164</FONT>            // number of clusters has to be smaller or equal the number of data points<a name="line.164"></a>
<FONT color="green">165</FONT>            if (points.size() &lt; k) {<a name="line.165"></a>
<FONT color="green">166</FONT>                throw new NumberIsTooSmallException(points.size(), k, false);<a name="line.166"></a>
<FONT color="green">167</FONT>            }<a name="line.167"></a>
<FONT color="green">168</FONT>    <a name="line.168"></a>
<FONT color="green">169</FONT>            // create the initial clusters<a name="line.169"></a>
<FONT color="green">170</FONT>            List&lt;Cluster&lt;T&gt;&gt; clusters = chooseInitialCenters(points, k, random);<a name="line.170"></a>
<FONT color="green">171</FONT>    <a name="line.171"></a>
<FONT color="green">172</FONT>            // create an array containing the latest assignment of a point to a cluster<a name="line.172"></a>
<FONT color="green">173</FONT>            // no need to initialize the array, as it will be filled with the first assignment<a name="line.173"></a>
<FONT color="green">174</FONT>            int[] assignments = new int[points.size()];<a name="line.174"></a>
<FONT color="green">175</FONT>            assignPointsToClusters(clusters, points, assignments);<a name="line.175"></a>
<FONT color="green">176</FONT>    <a name="line.176"></a>
<FONT color="green">177</FONT>            // iterate through updating the centers until we're done<a name="line.177"></a>
<FONT color="green">178</FONT>            final int max = (maxIterations &lt; 0) ? Integer.MAX_VALUE : maxIterations;<a name="line.178"></a>
<FONT color="green">179</FONT>            for (int count = 0; count &lt; max; count++) {<a name="line.179"></a>
<FONT color="green">180</FONT>                boolean emptyCluster = false;<a name="line.180"></a>
<FONT color="green">181</FONT>                List&lt;Cluster&lt;T&gt;&gt; newClusters = new ArrayList&lt;Cluster&lt;T&gt;&gt;();<a name="line.181"></a>
<FONT color="green">182</FONT>                for (final Cluster&lt;T&gt; cluster : clusters) {<a name="line.182"></a>
<FONT color="green">183</FONT>                    final T newCenter;<a name="line.183"></a>
<FONT color="green">184</FONT>                    if (cluster.getPoints().isEmpty()) {<a name="line.184"></a>
<FONT color="green">185</FONT>                        switch (emptyStrategy) {<a name="line.185"></a>
<FONT color="green">186</FONT>                            case LARGEST_VARIANCE :<a name="line.186"></a>
<FONT color="green">187</FONT>                                newCenter = getPointFromLargestVarianceCluster(clusters);<a name="line.187"></a>
<FONT color="green">188</FONT>                                break;<a name="line.188"></a>
<FONT color="green">189</FONT>                            case LARGEST_POINTS_NUMBER :<a name="line.189"></a>
<FONT color="green">190</FONT>                                newCenter = getPointFromLargestNumberCluster(clusters);<a name="line.190"></a>
<FONT color="green">191</FONT>                                break;<a name="line.191"></a>
<FONT color="green">192</FONT>                            case FARTHEST_POINT :<a name="line.192"></a>
<FONT color="green">193</FONT>                                newCenter = getFarthestPoint(clusters);<a name="line.193"></a>
<FONT color="green">194</FONT>                                break;<a name="line.194"></a>
<FONT color="green">195</FONT>                            default :<a name="line.195"></a>
<FONT color="green">196</FONT>                                throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS);<a name="line.196"></a>
<FONT color="green">197</FONT>                        }<a name="line.197"></a>
<FONT color="green">198</FONT>                        emptyCluster = true;<a name="line.198"></a>
<FONT color="green">199</FONT>                    } else {<a name="line.199"></a>
<FONT color="green">200</FONT>                        newCenter = cluster.getCenter().centroidOf(cluster.getPoints());<a name="line.200"></a>
<FONT color="green">201</FONT>                    }<a name="line.201"></a>
<FONT color="green">202</FONT>                    newClusters.add(new Cluster&lt;T&gt;(newCenter));<a name="line.202"></a>
<FONT color="green">203</FONT>                }<a name="line.203"></a>
<FONT color="green">204</FONT>                int changes = assignPointsToClusters(newClusters, points, assignments);<a name="line.204"></a>
<FONT color="green">205</FONT>                clusters = newClusters;<a name="line.205"></a>
<FONT color="green">206</FONT>    <a name="line.206"></a>
<FONT color="green">207</FONT>                // if there were no more changes in the point-to-cluster assignment<a name="line.207"></a>
<FONT color="green">208</FONT>                // and there are no empty clusters left, return the current clusters<a name="line.208"></a>
<FONT color="green">209</FONT>                if (changes == 0 &amp;&amp; !emptyCluster) {<a name="line.209"></a>
<FONT color="green">210</FONT>                    return clusters;<a name="line.210"></a>
<FONT color="green">211</FONT>                }<a name="line.211"></a>
<FONT color="green">212</FONT>            }<a name="line.212"></a>
<FONT color="green">213</FONT>            return clusters;<a name="line.213"></a>
<FONT color="green">214</FONT>        }<a name="line.214"></a>
<FONT color="green">215</FONT>    <a name="line.215"></a>
<FONT color="green">216</FONT>        /**<a name="line.216"></a>
<FONT color="green">217</FONT>         * Adds the given points to the closest {@link Cluster}.<a name="line.217"></a>
<FONT color="green">218</FONT>         *<a name="line.218"></a>
<FONT color="green">219</FONT>         * @param &lt;T&gt; type of the points to cluster<a name="line.219"></a>
<FONT color="green">220</FONT>         * @param clusters the {@link Cluster}s to add the points to<a name="line.220"></a>
<FONT color="green">221</FONT>         * @param points the points to add to the given {@link Cluster}s<a name="line.221"></a>
<FONT color="green">222</FONT>         * @param assignments points assignments to clusters<a name="line.222"></a>
<FONT color="green">223</FONT>         * @return the number of points assigned to different clusters as the iteration before<a name="line.223"></a>
<FONT color="green">224</FONT>         */<a name="line.224"></a>
<FONT color="green">225</FONT>        private static &lt;T extends Clusterable&lt;T&gt;&gt; int<a name="line.225"></a>
<FONT color="green">226</FONT>            assignPointsToClusters(final List&lt;Cluster&lt;T&gt;&gt; clusters, final Collection&lt;T&gt; points,<a name="line.226"></a>
<FONT color="green">227</FONT>                                   final int[] assignments) {<a name="line.227"></a>
<FONT color="green">228</FONT>            int assignedDifferently = 0;<a name="line.228"></a>
<FONT color="green">229</FONT>            int pointIndex = 0;<a name="line.229"></a>
<FONT color="green">230</FONT>            for (final T p : points) {<a name="line.230"></a>
<FONT color="green">231</FONT>                int clusterIndex = getNearestCluster(clusters, p);<a name="line.231"></a>
<FONT color="green">232</FONT>                if (clusterIndex != assignments[pointIndex]) {<a name="line.232"></a>
<FONT color="green">233</FONT>                    assignedDifferently++;<a name="line.233"></a>
<FONT color="green">234</FONT>                }<a name="line.234"></a>
<FONT color="green">235</FONT>    <a name="line.235"></a>
<FONT color="green">236</FONT>                Cluster&lt;T&gt; cluster = clusters.get(clusterIndex);<a name="line.236"></a>
<FONT color="green">237</FONT>                cluster.addPoint(p);<a name="line.237"></a>
<FONT color="green">238</FONT>                assignments[pointIndex++] = clusterIndex;<a name="line.238"></a>
<FONT color="green">239</FONT>            }<a name="line.239"></a>
<FONT color="green">240</FONT>    <a name="line.240"></a>
<FONT color="green">241</FONT>            return assignedDifferently;<a name="line.241"></a>
<FONT color="green">242</FONT>        }<a name="line.242"></a>
<FONT color="green">243</FONT>    <a name="line.243"></a>
<FONT color="green">244</FONT>        /**<a name="line.244"></a>
<FONT color="green">245</FONT>         * Use K-means++ to choose the initial centers.<a name="line.245"></a>
<FONT color="green">246</FONT>         *<a name="line.246"></a>
<FONT color="green">247</FONT>         * @param &lt;T&gt; type of the points to cluster<a name="line.247"></a>
<FONT color="green">248</FONT>         * @param points the points to choose the initial centers from<a name="line.248"></a>
<FONT color="green">249</FONT>         * @param k the number of centers to choose<a name="line.249"></a>
<FONT color="green">250</FONT>         * @param random random generator to use<a name="line.250"></a>
<FONT color="green">251</FONT>         * @return the initial centers<a name="line.251"></a>
<FONT color="green">252</FONT>         */<a name="line.252"></a>
<FONT color="green">253</FONT>        private static &lt;T extends Clusterable&lt;T&gt;&gt; List&lt;Cluster&lt;T&gt;&gt;<a name="line.253"></a>
<FONT color="green">254</FONT>            chooseInitialCenters(final Collection&lt;T&gt; points, final int k, final Random random) {<a name="line.254"></a>
<FONT color="green">255</FONT>    <a name="line.255"></a>
<FONT color="green">256</FONT>            // Convert to list for indexed access. Make it unmodifiable, since removal of items<a name="line.256"></a>
<FONT color="green">257</FONT>            // would screw up the logic of this method.<a name="line.257"></a>
<FONT color="green">258</FONT>            final List&lt;T&gt; pointList = Collections.unmodifiableList(new ArrayList&lt;T&gt; (points));<a name="line.258"></a>
<FONT color="green">259</FONT>    <a name="line.259"></a>
<FONT color="green">260</FONT>            // The number of points in the list.<a name="line.260"></a>
<FONT color="green">261</FONT>            final int numPoints = pointList.size();<a name="line.261"></a>
<FONT color="green">262</FONT>    <a name="line.262"></a>
<FONT color="green">263</FONT>            // Set the corresponding element in this array to indicate when<a name="line.263"></a>
<FONT color="green">264</FONT>            // elements of pointList are no longer available.<a name="line.264"></a>
<FONT color="green">265</FONT>            final boolean[] taken = new boolean[numPoints];<a name="line.265"></a>
<FONT color="green">266</FONT>    <a name="line.266"></a>
<FONT color="green">267</FONT>            // The resulting list of initial centers.<a name="line.267"></a>
<FONT color="green">268</FONT>            final List&lt;Cluster&lt;T&gt;&gt; resultSet = new ArrayList&lt;Cluster&lt;T&gt;&gt;();<a name="line.268"></a>
<FONT color="green">269</FONT>    <a name="line.269"></a>
<FONT color="green">270</FONT>            // Choose one center uniformly at random from among the data points.<a name="line.270"></a>
<FONT color="green">271</FONT>            final int firstPointIndex = random.nextInt(numPoints);<a name="line.271"></a>
<FONT color="green">272</FONT>    <a name="line.272"></a>
<FONT color="green">273</FONT>            final T firstPoint = pointList.get(firstPointIndex);<a name="line.273"></a>
<FONT color="green">274</FONT>    <a name="line.274"></a>
<FONT color="green">275</FONT>            resultSet.add(new Cluster&lt;T&gt;(firstPoint));<a name="line.275"></a>
<FONT color="green">276</FONT>    <a name="line.276"></a>
<FONT color="green">277</FONT>            // Must mark it as taken<a name="line.277"></a>
<FONT color="green">278</FONT>            taken[firstPointIndex] = true;<a name="line.278"></a>
<FONT color="green">279</FONT>    <a name="line.279"></a>
<FONT color="green">280</FONT>            // To keep track of the minimum distance squared of elements of<a name="line.280"></a>
<FONT color="green">281</FONT>            // pointList to elements of resultSet.<a name="line.281"></a>
<FONT color="green">282</FONT>            final double[] minDistSquared = new double[numPoints];<a name="line.282"></a>
<FONT color="green">283</FONT>    <a name="line.283"></a>
<FONT color="green">284</FONT>            // Initialize the elements.  Since the only point in resultSet is firstPoint,<a name="line.284"></a>
<FONT color="green">285</FONT>            // this is very easy.<a name="line.285"></a>
<FONT color="green">286</FONT>            for (int i = 0; i &lt; numPoints; i++) {<a name="line.286"></a>
<FONT color="green">287</FONT>                if (i != firstPointIndex) { // That point isn't considered<a name="line.287"></a>
<FONT color="green">288</FONT>                    double d = firstPoint.distanceFrom(pointList.get(i));<a name="line.288"></a>
<FONT color="green">289</FONT>                    minDistSquared[i] = d*d;<a name="line.289"></a>
<FONT color="green">290</FONT>                }<a name="line.290"></a>
<FONT color="green">291</FONT>            }<a name="line.291"></a>
<FONT color="green">292</FONT>    <a name="line.292"></a>
<FONT color="green">293</FONT>            while (resultSet.size() &lt; k) {<a name="line.293"></a>
<FONT color="green">294</FONT>    <a name="line.294"></a>
<FONT color="green">295</FONT>                // Sum up the squared distances for the points in pointList not<a name="line.295"></a>
<FONT color="green">296</FONT>                // already taken.<a name="line.296"></a>
<FONT color="green">297</FONT>                double distSqSum = 0.0;<a name="line.297"></a>
<FONT color="green">298</FONT>    <a name="line.298"></a>
<FONT color="green">299</FONT>                for (int i = 0; i &lt; numPoints; i++) {<a name="line.299"></a>
<FONT color="green">300</FONT>                    if (!taken[i]) {<a name="line.300"></a>
<FONT color="green">301</FONT>                        distSqSum += minDistSquared[i];<a name="line.301"></a>
<FONT color="green">302</FONT>                    }<a name="line.302"></a>
<FONT color="green">303</FONT>                }<a name="line.303"></a>
<FONT color="green">304</FONT>    <a name="line.304"></a>
<FONT color="green">305</FONT>                // Add one new data point as a center. Each point x is chosen with<a name="line.305"></a>
<FONT color="green">306</FONT>                // probability proportional to D(x)2<a name="line.306"></a>
<FONT color="green">307</FONT>                final double r = random.nextDouble() * distSqSum;<a name="line.307"></a>
<FONT color="green">308</FONT>    <a name="line.308"></a>
<FONT color="green">309</FONT>                // The index of the next point to be added to the resultSet.<a name="line.309"></a>
<FONT color="green">310</FONT>                int nextPointIndex = -1;<a name="line.310"></a>
<FONT color="green">311</FONT>    <a name="line.311"></a>
<FONT color="green">312</FONT>                // Sum through the squared min distances again, stopping when<a name="line.312"></a>
<FONT color="green">313</FONT>                // sum &gt;= r.<a name="line.313"></a>
<FONT color="green">314</FONT>                double sum = 0.0;<a name="line.314"></a>
<FONT color="green">315</FONT>                for (int i = 0; i &lt; numPoints; i++) {<a name="line.315"></a>
<FONT color="green">316</FONT>                    if (!taken[i]) {<a name="line.316"></a>
<FONT color="green">317</FONT>                        sum += minDistSquared[i];<a name="line.317"></a>
<FONT color="green">318</FONT>                        if (sum &gt;= r) {<a name="line.318"></a>
<FONT color="green">319</FONT>                            nextPointIndex = i;<a name="line.319"></a>
<FONT color="green">320</FONT>                            break;<a name="line.320"></a>
<FONT color="green">321</FONT>                        }<a name="line.321"></a>
<FONT color="green">322</FONT>                    }<a name="line.322"></a>
<FONT color="green">323</FONT>                }<a name="line.323"></a>
<FONT color="green">324</FONT>    <a name="line.324"></a>
<FONT color="green">325</FONT>                // If it's not set to &gt;= 0, the point wasn't found in the previous<a name="line.325"></a>
<FONT color="green">326</FONT>                // for loop, probably because distances are extremely small.  Just pick<a name="line.326"></a>
<FONT color="green">327</FONT>                // the last available point.<a name="line.327"></a>
<FONT color="green">328</FONT>                if (nextPointIndex == -1) {<a name="line.328"></a>
<FONT color="green">329</FONT>                    for (int i = numPoints - 1; i &gt;= 0; i--) {<a name="line.329"></a>
<FONT color="green">330</FONT>                        if (!taken[i]) {<a name="line.330"></a>
<FONT color="green">331</FONT>                            nextPointIndex = i;<a name="line.331"></a>
<FONT color="green">332</FONT>                            break;<a name="line.332"></a>
<FONT color="green">333</FONT>                        }<a name="line.333"></a>
<FONT color="green">334</FONT>                    }<a name="line.334"></a>
<FONT color="green">335</FONT>                }<a name="line.335"></a>
<FONT color="green">336</FONT>    <a name="line.336"></a>
<FONT color="green">337</FONT>                // We found one.<a name="line.337"></a>
<FONT color="green">338</FONT>                if (nextPointIndex &gt;= 0) {<a name="line.338"></a>
<FONT color="green">339</FONT>    <a name="line.339"></a>
<FONT color="green">340</FONT>                    final T p = pointList.get(nextPointIndex);<a name="line.340"></a>
<FONT color="green">341</FONT>    <a name="line.341"></a>
<FONT color="green">342</FONT>                    resultSet.add(new Cluster&lt;T&gt; (p));<a name="line.342"></a>
<FONT color="green">343</FONT>    <a name="line.343"></a>
<FONT color="green">344</FONT>                    // Mark it as taken.<a name="line.344"></a>
<FONT color="green">345</FONT>                    taken[nextPointIndex] = true;<a name="line.345"></a>
<FONT color="green">346</FONT>    <a name="line.346"></a>
<FONT color="green">347</FONT>                    if (resultSet.size() &lt; k) {<a name="line.347"></a>
<FONT color="green">348</FONT>                        // Now update elements of minDistSquared.  We only have to compute<a name="line.348"></a>
<FONT color="green">349</FONT>                        // the distance to the new center to do this.<a name="line.349"></a>
<FONT color="green">350</FONT>                        for (int j = 0; j &lt; numPoints; j++) {<a name="line.350"></a>
<FONT color="green">351</FONT>                            // Only have to worry about the points still not taken.<a name="line.351"></a>
<FONT color="green">352</FONT>                            if (!taken[j]) {<a name="line.352"></a>
<FONT color="green">353</FONT>                                double d = p.distanceFrom(pointList.get(j));<a name="line.353"></a>
<FONT color="green">354</FONT>                                double d2 = d * d;<a name="line.354"></a>
<FONT color="green">355</FONT>                                if (d2 &lt; minDistSquared[j]) {<a name="line.355"></a>
<FONT color="green">356</FONT>                                    minDistSquared[j] = d2;<a name="line.356"></a>
<FONT color="green">357</FONT>                                }<a name="line.357"></a>
<FONT color="green">358</FONT>                            }<a name="line.358"></a>
<FONT color="green">359</FONT>                        }<a name="line.359"></a>
<FONT color="green">360</FONT>                    }<a name="line.360"></a>
<FONT color="green">361</FONT>    <a name="line.361"></a>
<FONT color="green">362</FONT>                } else {<a name="line.362"></a>
<FONT color="green">363</FONT>                    // None found --<a name="line.363"></a>
<FONT color="green">364</FONT>                    // Break from the while loop to prevent<a name="line.364"></a>
<FONT color="green">365</FONT>                    // an infinite loop.<a name="line.365"></a>
<FONT color="green">366</FONT>                    break;<a name="line.366"></a>
<FONT color="green">367</FONT>                }<a name="line.367"></a>
<FONT color="green">368</FONT>            }<a name="line.368"></a>
<FONT color="green">369</FONT>    <a name="line.369"></a>
<FONT color="green">370</FONT>            return resultSet;<a name="line.370"></a>
<FONT color="green">371</FONT>        }<a name="line.371"></a>
<FONT color="green">372</FONT>    <a name="line.372"></a>
<FONT color="green">373</FONT>        /**<a name="line.373"></a>
<FONT color="green">374</FONT>         * Get a random point from the {@link Cluster} with the largest distance variance.<a name="line.374"></a>
<FONT color="green">375</FONT>         *<a name="line.375"></a>
<FONT color="green">376</FONT>         * @param clusters the {@link Cluster}s to search<a name="line.376"></a>
<FONT color="green">377</FONT>         * @return a random point from the selected cluster<a name="line.377"></a>
<FONT color="green">378</FONT>         * @throws ConvergenceException if clusters are all empty<a name="line.378"></a>
<FONT color="green">379</FONT>         */<a name="line.379"></a>
<FONT color="green">380</FONT>        private T getPointFromLargestVarianceCluster(final Collection&lt;Cluster&lt;T&gt;&gt; clusters)<a name="line.380"></a>
<FONT color="green">381</FONT>        throws ConvergenceException {<a name="line.381"></a>
<FONT color="green">382</FONT>    <a name="line.382"></a>
<FONT color="green">383</FONT>            double maxVariance = Double.NEGATIVE_INFINITY;<a name="line.383"></a>
<FONT color="green">384</FONT>            Cluster&lt;T&gt; selected = null;<a name="line.384"></a>
<FONT color="green">385</FONT>            for (final Cluster&lt;T&gt; cluster : clusters) {<a name="line.385"></a>
<FONT color="green">386</FONT>                if (!cluster.getPoints().isEmpty()) {<a name="line.386"></a>
<FONT color="green">387</FONT>    <a name="line.387"></a>
<FONT color="green">388</FONT>                    // compute the distance variance of the current cluster<a name="line.388"></a>
<FONT color="green">389</FONT>                    final T center = cluster.getCenter();<a name="line.389"></a>
<FONT color="green">390</FONT>                    final Variance stat = new Variance();<a name="line.390"></a>
<FONT color="green">391</FONT>                    for (final T point : cluster.getPoints()) {<a name="line.391"></a>
<FONT color="green">392</FONT>                        stat.increment(point.distanceFrom(center));<a name="line.392"></a>
<FONT color="green">393</FONT>                    }<a name="line.393"></a>
<FONT color="green">394</FONT>                    final double variance = stat.getResult();<a name="line.394"></a>
<FONT color="green">395</FONT>    <a name="line.395"></a>
<FONT color="green">396</FONT>                    // select the cluster with the largest variance<a name="line.396"></a>
<FONT color="green">397</FONT>                    if (variance &gt; maxVariance) {<a name="line.397"></a>
<FONT color="green">398</FONT>                        maxVariance = variance;<a name="line.398"></a>
<FONT color="green">399</FONT>                        selected = cluster;<a name="line.399"></a>
<FONT color="green">400</FONT>                    }<a name="line.400"></a>
<FONT color="green">401</FONT>    <a name="line.401"></a>
<FONT color="green">402</FONT>                }<a name="line.402"></a>
<FONT color="green">403</FONT>            }<a name="line.403"></a>
<FONT color="green">404</FONT>    <a name="line.404"></a>
<FONT color="green">405</FONT>            // did we find at least one non-empty cluster ?<a name="line.405"></a>
<FONT color="green">406</FONT>            if (selected == null) {<a name="line.406"></a>
<FONT color="green">407</FONT>                throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS);<a name="line.407"></a>
<FONT color="green">408</FONT>            }<a name="line.408"></a>
<FONT color="green">409</FONT>    <a name="line.409"></a>
<FONT color="green">410</FONT>            // extract a random point from the cluster<a name="line.410"></a>
<FONT color="green">411</FONT>            final List&lt;T&gt; selectedPoints = selected.getPoints();<a name="line.411"></a>
<FONT color="green">412</FONT>            return selectedPoints.remove(random.nextInt(selectedPoints.size()));<a name="line.412"></a>
<FONT color="green">413</FONT>    <a name="line.413"></a>
<FONT color="green">414</FONT>        }<a name="line.414"></a>
<FONT color="green">415</FONT>    <a name="line.415"></a>
<FONT color="green">416</FONT>        /**<a name="line.416"></a>
<FONT color="green">417</FONT>         * Get a random point from the {@link Cluster} with the largest number of points<a name="line.417"></a>
<FONT color="green">418</FONT>         *<a name="line.418"></a>
<FONT color="green">419</FONT>         * @param clusters the {@link Cluster}s to search<a name="line.419"></a>
<FONT color="green">420</FONT>         * @return a random point from the selected cluster<a name="line.420"></a>
<FONT color="green">421</FONT>         * @throws ConvergenceException if clusters are all empty<a name="line.421"></a>
<FONT color="green">422</FONT>         */<a name="line.422"></a>
<FONT color="green">423</FONT>        private T getPointFromLargestNumberCluster(final Collection&lt;Cluster&lt;T&gt;&gt; clusters) throws ConvergenceException {<a name="line.423"></a>
<FONT color="green">424</FONT>    <a name="line.424"></a>
<FONT color="green">425</FONT>            int maxNumber = 0;<a name="line.425"></a>
<FONT color="green">426</FONT>            Cluster&lt;T&gt; selected = null;<a name="line.426"></a>
<FONT color="green">427</FONT>            for (final Cluster&lt;T&gt; cluster : clusters) {<a name="line.427"></a>
<FONT color="green">428</FONT>    <a name="line.428"></a>
<FONT color="green">429</FONT>                // get the number of points of the current cluster<a name="line.429"></a>
<FONT color="green">430</FONT>                final int number = cluster.getPoints().size();<a name="line.430"></a>
<FONT color="green">431</FONT>    <a name="line.431"></a>
<FONT color="green">432</FONT>                // select the cluster with the largest number of points<a name="line.432"></a>
<FONT color="green">433</FONT>                if (number &gt; maxNumber) {<a name="line.433"></a>
<FONT color="green">434</FONT>                    maxNumber = number;<a name="line.434"></a>
<FONT color="green">435</FONT>                    selected = cluster;<a name="line.435"></a>
<FONT color="green">436</FONT>                }<a name="line.436"></a>
<FONT color="green">437</FONT>    <a name="line.437"></a>
<FONT color="green">438</FONT>            }<a name="line.438"></a>
<FONT color="green">439</FONT>    <a name="line.439"></a>
<FONT color="green">440</FONT>            // did we find at least one non-empty cluster ?<a name="line.440"></a>
<FONT color="green">441</FONT>            if (selected == null) {<a name="line.441"></a>
<FONT color="green">442</FONT>                throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS);<a name="line.442"></a>
<FONT color="green">443</FONT>            }<a name="line.443"></a>
<FONT color="green">444</FONT>    <a name="line.444"></a>
<FONT color="green">445</FONT>            // extract a random point from the cluster<a name="line.445"></a>
<FONT color="green">446</FONT>            final List&lt;T&gt; selectedPoints = selected.getPoints();<a name="line.446"></a>
<FONT color="green">447</FONT>            return selectedPoints.remove(random.nextInt(selectedPoints.size()));<a name="line.447"></a>
<FONT color="green">448</FONT>    <a name="line.448"></a>
<FONT color="green">449</FONT>        }<a name="line.449"></a>
<FONT color="green">450</FONT>    <a name="line.450"></a>
<FONT color="green">451</FONT>        /**<a name="line.451"></a>
<FONT color="green">452</FONT>         * Get the point farthest to its cluster center<a name="line.452"></a>
<FONT color="green">453</FONT>         *<a name="line.453"></a>
<FONT color="green">454</FONT>         * @param clusters the {@link Cluster}s to search<a name="line.454"></a>
<FONT color="green">455</FONT>         * @return point farthest to its cluster center<a name="line.455"></a>
<FONT color="green">456</FONT>         * @throws ConvergenceException if clusters are all empty<a name="line.456"></a>
<FONT color="green">457</FONT>         */<a name="line.457"></a>
<FONT color="green">458</FONT>        private T getFarthestPoint(final Collection&lt;Cluster&lt;T&gt;&gt; clusters) throws ConvergenceException {<a name="line.458"></a>
<FONT color="green">459</FONT>    <a name="line.459"></a>
<FONT color="green">460</FONT>            double maxDistance = Double.NEGATIVE_INFINITY;<a name="line.460"></a>
<FONT color="green">461</FONT>            Cluster&lt;T&gt; selectedCluster = null;<a name="line.461"></a>
<FONT color="green">462</FONT>            int selectedPoint = -1;<a name="line.462"></a>
<FONT color="green">463</FONT>            for (final Cluster&lt;T&gt; cluster : clusters) {<a name="line.463"></a>
<FONT color="green">464</FONT>    <a name="line.464"></a>
<FONT color="green">465</FONT>                // get the farthest point<a name="line.465"></a>
<FONT color="green">466</FONT>                final T center = cluster.getCenter();<a name="line.466"></a>
<FONT color="green">467</FONT>                final List&lt;T&gt; points = cluster.getPoints();<a name="line.467"></a>
<FONT color="green">468</FONT>                for (int i = 0; i &lt; points.size(); ++i) {<a name="line.468"></a>
<FONT color="green">469</FONT>                    final double distance = points.get(i).distanceFrom(center);<a name="line.469"></a>
<FONT color="green">470</FONT>                    if (distance &gt; maxDistance) {<a name="line.470"></a>
<FONT color="green">471</FONT>                        maxDistance     = distance;<a name="line.471"></a>
<FONT color="green">472</FONT>                        selectedCluster = cluster;<a name="line.472"></a>
<FONT color="green">473</FONT>                        selectedPoint   = i;<a name="line.473"></a>
<FONT color="green">474</FONT>                    }<a name="line.474"></a>
<FONT color="green">475</FONT>                }<a name="line.475"></a>
<FONT color="green">476</FONT>    <a name="line.476"></a>
<FONT color="green">477</FONT>            }<a name="line.477"></a>
<FONT color="green">478</FONT>    <a name="line.478"></a>
<FONT color="green">479</FONT>            // did we find at least one non-empty cluster ?<a name="line.479"></a>
<FONT color="green">480</FONT>            if (selectedCluster == null) {<a name="line.480"></a>
<FONT color="green">481</FONT>                throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS);<a name="line.481"></a>
<FONT color="green">482</FONT>            }<a name="line.482"></a>
<FONT color="green">483</FONT>    <a name="line.483"></a>
<FONT color="green">484</FONT>            return selectedCluster.getPoints().remove(selectedPoint);<a name="line.484"></a>
<FONT color="green">485</FONT>    <a name="line.485"></a>
<FONT color="green">486</FONT>        }<a name="line.486"></a>
<FONT color="green">487</FONT>    <a name="line.487"></a>
<FONT color="green">488</FONT>        /**<a name="line.488"></a>
<FONT color="green">489</FONT>         * Returns the nearest {@link Cluster} to the given point<a name="line.489"></a>
<FONT color="green">490</FONT>         *<a name="line.490"></a>
<FONT color="green">491</FONT>         * @param &lt;T&gt; type of the points to cluster<a name="line.491"></a>
<FONT color="green">492</FONT>         * @param clusters the {@link Cluster}s to search<a name="line.492"></a>
<FONT color="green">493</FONT>         * @param point the point to find the nearest {@link Cluster} for<a name="line.493"></a>
<FONT color="green">494</FONT>         * @return the index of the nearest {@link Cluster} to the given point<a name="line.494"></a>
<FONT color="green">495</FONT>         */<a name="line.495"></a>
<FONT color="green">496</FONT>        private static &lt;T extends Clusterable&lt;T&gt;&gt; int<a name="line.496"></a>
<FONT color="green">497</FONT>            getNearestCluster(final Collection&lt;Cluster&lt;T&gt;&gt; clusters, final T point) {<a name="line.497"></a>
<FONT color="green">498</FONT>            double minDistance = Double.MAX_VALUE;<a name="line.498"></a>
<FONT color="green">499</FONT>            int clusterIndex = 0;<a name="line.499"></a>
<FONT color="green">500</FONT>            int minCluster = 0;<a name="line.500"></a>
<FONT color="green">501</FONT>            for (final Cluster&lt;T&gt; c : clusters) {<a name="line.501"></a>
<FONT color="green">502</FONT>                final double distance = point.distanceFrom(c.getCenter());<a name="line.502"></a>
<FONT color="green">503</FONT>                if (distance &lt; minDistance) {<a name="line.503"></a>
<FONT color="green">504</FONT>                    minDistance = distance;<a name="line.504"></a>
<FONT color="green">505</FONT>                    minCluster = clusterIndex;<a name="line.505"></a>
<FONT color="green">506</FONT>                }<a name="line.506"></a>
<FONT color="green">507</FONT>                clusterIndex++;<a name="line.507"></a>
<FONT color="green">508</FONT>            }<a name="line.508"></a>
<FONT color="green">509</FONT>            return minCluster;<a name="line.509"></a>
<FONT color="green">510</FONT>        }<a name="line.510"></a>
<FONT color="green">511</FONT>    <a name="line.511"></a>
<FONT color="green">512</FONT>    }<a name="line.512"></a>




























































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